Nearest-Neighbor Scores for Doublet Detection

Why Local Proximity Can Indicate Doublet Evidence

An artificial doublet is constructed to approximate the combined expression profile of two cells. If those cells have distinct expression patterns, their combined profile may lie between the corresponding singlet populations or in a region of expression space with few observed singlets. A nearest-neighbor method asks whether an observed barcode is close to many artificial doublets in that space. The answer is a local score: useful for ranking barcodes by evidence, but not by itself a probability or a decision to remove a barcode.

The preceding material on artificial doublets establishes how simulated profiles can be formed from observed cells. Here, the focus is how those profiles contribute to a neighborhood score. The method depends on treating simulated and observed barcodes comparably: they must be represented using the same selected features, transformations, and embedding. If their distances are not meaningful, counting their neighbors will not provide meaningful evidence.

Constructing Comparable Neighborhoods

A typical analysis begins with observed cell-associated barcodes and a set of simulated artificial doublets. A simulated profile may be made by adding the count vectors of two sampled observed barcodes. Observed and simulated profiles are then processed together so that the same genes, normalization, feature selection, and dimensionality reduction define their coordinates. A distance—often Euclidean distance in selected principal-component coordinates—is used to find neighbors.

The query barcode itself should not count as one of its own neighbors. Otherwise, each observed query would have at least one observed neighbor simply because it is present in the data, changing the denominator or displacing a relevant nearby point. The same neighborhood rule should be used consistently for every query. If several points have tied distances at the \(k\)-th position, a reproducible tie-breaking rule is needed.

The score relies on several substantive assumptions. First, artificial doublets should resemble the profiles that real doublets would produce under the experiment’s count-generation and preprocessing pipeline. Second, the observed cells sampled to construct them should adequately represent the cell populations that could contribute to doublets. Third, the chosen representation and distance should preserve local distinctions relevant to mixed-cell profiles. Finally, technical structure such as sample or batch effects should not dominate the distances in a way that makes neighbors reflect processing artifacts rather than expression similarity.

These assumptions are approximations, not guarantees. For example, summing two observed count vectors can create a reasonable artificial profile, but normalization and projection can still place it differently from a real doublet. The score is only as informative as the simulation and geometry that produced it.

Raw Scores and Simulation-Ratio Adjustment

The raw score depends on how many simulated profiles were added. If artificial doublets make up a large fraction of the combined data, a barcode may have many simulated neighbors even when its neighborhood is no more enriched for simulations than the overall data. Let \(q\) denote the fraction of all points in the combined observed-and-simulated set that are simulated. A commonly used adjustment centers the raw score at this global fraction and rescales its maximum:

This adjustment gives \(a_i=0\) when \(f_i=q\), the global simulated fraction, and \(a_i=1\) when every one of the barcode’s neighbors is simulated. It can be negative when the local simulated fraction is below the global fraction. The adjustment is an enrichment index, not an estimated probability that barcode \(i\) is a doublet. In particular, it does not correct a poor simulation or an uninformative embedding.

What the Adjustment Does—and Does Not—Establish

The adjustment follows directly from two chosen reference points. When the local simulated fraction equals the global fraction \(q\), the adjusted score should be zero. When the local fraction is one, it should be one. An affine transformation \(a_i=c f_i+d\) satisfying those conditions has \(d=-cq\) and \(c(1-q)=1\). Therefore \(c=1/(1-q)\) and \(d=-q/(1-q)\), which gives \(a_i=(f_i-q)/(1-q)\).

This argument justifies the scaling, but it does not establish that \(a_i\) is a calibrated measure of a barcode’s true doublet status. The raw fraction estimates the composition of a finite neighborhood in the augmented dataset. The adjustment accounts for the chosen global simulation fraction; it does not turn synthetic labels into known labels for real barcodes. It also does not remove sampling variability: when \(k\) is small, changing one neighbor changes the raw score by \(1/k\).

Choosing \(k\) and Reading the Ranking

The neighborhood size \(k\) controls the scale of the comparison. A small \(k\) is sensitive to very local structure, but each neighbor has a large effect on the score and random variation can be substantial. A larger \(k\) averages over more points and can stabilize the fraction, but may combine distinct cell populations or blur a small region of doublet-like profiles. There is no universally correct \(k\); it should be selected with the data size, representation, and intended use in mind.

A score is generally used to rank observed barcodes, with higher scores indicating greater local enrichment for artificial doublets relative to the simulation fraction. Rankings can be compared across parameter settings as a sensitivity check, but raw values from different simulation ratios or embeddings need not be directly comparable. The number of artificial profiles, their sampling procedure, and the fraction \(q\) should be recorded when reporting scores.

Diagnostics, Alternatives, and Limitations

A useful diagnostic is to inspect the score distribution and the locations of high-scoring barcodes in the embedding. If artificial profiles are well represented, some should occur near regions of observed data with mixed or intermediate expression patterns. If nearly all observed barcodes have similar scores, the method may have little ranking information, or the chosen \(k\) and embedding may be too coarse. If scores change sharply under modest changes to \(k\), the ranking is sensitive to neighborhood boundaries. If simulated profiles cluster separately from all observed profiles, the score may largely distinguish the simulation procedure rather than identify plausible real doublets.

Repeat the calculation across reasonable choices of neighborhood size, number of retained dimensions, and artificial-doublet sampling. Check whether the highest-ranked barcodes remain broadly similar. Also examine whether neighborhoods are dominated by sample or batch membership. A distance-based score can be high because of technical structure, unusual cell states, or poor representation—not only because of doublet-like expression.

Nearest-neighbor scoring is one approach among several. A direct classifier would require suitable labeled examples and can learn the limitations of those labels; artificial doublets provide training-like examples but are still approximations. A cluster-level comparison summarizes groups and can miss barcode-level local variation. The nearest-neighbor method avoids requiring a global linear boundary, but its results depend on the chosen metric and representation. No one approach makes synthetic doublets equivalent to validated real doublets.

A common mistake is to read a score of \(0.8\) as an 80% chance that the barcode is a doublet. That is incorrect: the score is a fraction of simulated neighbors (or a rescaled version of that fraction), and its value depends on the augmented dataset and analysis choices. Interpret it as relative local evidence, then use appropriate validation and decision procedures rather than treating the score itself as a probability or a removal rule.